Question 1 Briey argue that that the following functions are differentiable at (513,11, 3) = (1, 2, 1) (what result are you using?) and compute D f (1, 2, 1) for each. (a) f (32,31, 2) = (10g(x),sin(z)) (recall that log :1n)_ (b) f(x,y,z) = lyl +e\". Question 2 Let g: R3 > R2 be given by 9(33, y, z) = (y cos(z), efz) and let f: R2 > R2 be given by f(u,v) = (uv,u2(v 7r)). (a) Briey argue that g and f are differentiable everywhere (i.e., at any a: 6 R3), and use this to argue that h = f o g (i.e., the function given by h(a:,y,z) = f(g(sc,y,z))) is differentiable everywhere. (b) Use the chain rule to compute Dh(0, 2, 7r)